>> Mathematical logic is not all of logic, but it is logic, not> mathematics. There is more to the logic which is used by> mathematicians, such as in metamathematics, than is in the> first order predicate calculus, which is what is used in> mathematical proofs. There are metamathematical proofs of> mathematical theorems which do not have mathematical proofs.>> There is also inductive logic, which is best represented by> statistical decision theory, and there are modal logics. I> have seen description of "quantum logics", but I do not see> them as more than partial representations.

What is mathematical logic? Is it logic studied with mathematical tools? (Which might be any logic at all.) Or is that part of logic that underlies mathematical reasoning? Or something else?